91Ó°ÊÓ

Systems that have no solution are called ____ systems.

Discuss/Explain why Cramer's rule cannot be applied if \(D=0 .\) Use an example to illustrate.

Determine whether the ordered pairs given are solutions. $$3 x-y>5 ;(0,0),(4,-1),(-1,-5),(1,-2)$$

Solve each system of inequalities by graphing the solution region. Verify the solution using a test point. $$\left\\{\begin{array}{c}x+2 y \geq 1 \\ 2 x-y \leq-2\end{array}\right.$$

Decompose each rational expression into partial fractions using convenient values. $$\frac{-11 x+6}{5 x^{2}-4 x-12}$$

Find the area of the parallelogram with vertices given (Hint: Use two triangles.) Assume units are in \(\mathrm{ft}\). $$(-5,-6),(5,0),(5,4), \text { and }(-5,-2)$$

Decompose each rational expression into partial fractions using convenient values. $$\frac{x^{2}+24 x-12}{x^{3}-4 x}$$

The volume of a triangular pyramid is given by the formula \(V=\frac{1}{3} B h,\) where \(B\) represents the area of the triangular base and \(h\) is the height of the pyramid. Find the volume of a triangular pyramid whose height is given and whose base has the coordinates shown. Assume units are in m. $$h=6 \mathrm{m} ; \text { vertices }(3,5),(-4,2), \text { and }(-1,6)$$

The volume of a triangular pyramid is given by the formula \(V=\frac{1}{3} B h,\) where \(B\) represents the area of the triangular base and \(h\) is the height of the pyramid. Find the volume of a triangular pyramid whose height is given and whose base has the coordinates shown. Assume units are in m. $$h=7.5 \mathrm{m} ; \text { vertices }(-2,3),(-3,-4), \text { and }(-6,1)$$

Write each system as a matrix equation and solve (if possible) using inverse matrices and your calculator. If the coefficient matrix is singular, write no solution. $$\left\\{\begin{array}{l} 0.05 x-3.2 y=-15.8 \\ 0.02 x+2.4 y=12.08 \end{array}\right.$$